Cyclic prefix schemes

ABSTRACT

Methods and systems are proposed for transmitting data from a source ( 110 ) to a destination ( 130 ) via a relay station ( 120 ) having multiple antennae ( 122, 124 ). The relay station ( 120 ) receives from the source a message containing the data and a first cyclic prefix. It does this using each of its antennae ( 122, 124 ), so producing multiple respective received signals. In certain embodiments, the relay station ( 120 ) removes the first cyclic prefix from the received signals, replacing it with a new one. In other embodiments, the relay station ( 120 ) removes only a portion of the first cyclic prefix. In either case, the relay station ( 120 ) may apply space-time coding to generate second signals, which it transmits to the destination ( 130 ), which extracts the data. Methods are also proposed for estimating parameters of the channel, to enable the destination ( 130 ) to decode the data.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is one of two patent applications claimingpriority from U.S. provisional patent application No. 61/089,617. Thepresent patent application relates to the usage of cyclic prefixes,whereas the other patent application relates to techniques forspace-time coding. The techniques described in the respective two patentapplications are independent since either can be used without the other,although it is equally possible to construct systems which combinetechniques from the respective two patent applications.

FIELD OF THE INVENTION

This invention relates to methods and systems for implementing cyclicprefixes in a wireless communication channel comprising a relay stationcapable of performing information coding, particularly but notexclusively, analog space-time coding.

BACKGROUND OF THE INVENTION

Wireless relays have shown potential for extending communication rangeand providing good quality of experience. In a typical wirelesscommunication system utilizing relays, the relay station would be timeshared between different sources and destination. In such a scenario,the relay station needs to estimate the Angular Carrier Frequency Offset(ACFO) present between each pair of source and relay antennae (denotedACFO φ_(r)). The ACFO that is present between each pair of relay anddestination antennae (denoted ACFO φ_(d)) will be compensated for at thedestination.

Joint compensation of the source to relay and relay to destination ACFOis not possible in the prior art. Compensation for the source to relayACFO φ_(r) can thus only be performed at the relay station. The relaystation of the prior art will need to estimate and compensate the ACFOfor each source-and-relay pair and this complicates the relay stationhardware and increases the power required by the relay station.

Implementations of analog space-time coding (ASTC) in the prior art alsohave the limitation that the transmission channel has to be flat fading.This is because inter-symbol interference (ISI) results when thetransmission channel has frequency selective fading. The insertion of acyclic prefix (CP) can be used to mitigate against ISI. The cyclicprefix inserted should preferably be of a length greater than that ofthe channel impulse response (CIR).

Typical implementations of ASTC also require that the samples within asignal be re-ordered when performing the coding.

It is an object of the present invention to provide a method forimplementing cyclic prefixes and compensating for the channel effects ofa wireless communication channel, which addresses at least one of theproblems of the prior art and/or to provide the public with a usefulchoice.

SUMMARY OF THE INVENTION

In general terms, the present invention relates to transmitting datathough a wireless communication channel from a source to a destinationvia a relay station having multiple antennae. The relay station receivesa message from the source containing the data and a first cyclic prefix.It does this using each of its antennae, so producing multiplerespective received signals. In a first aspect of the invention, therelay station removes the first cyclic prefix from the received signals,replacing it with a new one. In a second aspect of the invention, therelay station removes only a portion of the first cyclic prefix. Ineither case, the relay station may apply space-time coding to generatesecond signals, which it transmits to the destination, which extractsthe data. A further aspect of the invention relates to estimatingparameters of the channel, to enable the destination to decode the data.

The invention may be expressed alternatively as an integrated circuitconfigured to enable the above mentioned aspects of the invention.

The cyclic prefix schemes of the present invention do not require thatthe transmission channels be flat fading.

BRIEF DESCRIPTION OF THE DRAWINGS

By way of example only, embodiments will be described with reference tothe accompanying drawings, in which:

FIG. 1 is a schematic drawing of a communication channel having a sourcestation S, relay station R and destination station D, according to anembodiment of the invention;

FIG. 2 is a flow diagram of a scheme for inserting cyclic prefixesaccording to a Cyclic Prefix Scheme 1 of the example embodiment;

FIG. 3 is a flow diagram of a scheme for inserting cyclic prefixesaccording to a Cyclic Prefix Scheme 2 of the example embodiment;

FIG. 4 is a flow diagram of a method for performing channel estimationaccording to the example embodiment;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows a communication channel according to an example embodiment.This channel consists of a source station/node 110 (S), a relay station120 (R) and a destination station/node 130 (D). The source and thedestination each have only one antenna, and the relay station 120 hastwo antennae 122,124. The antennae at the source station/node 110, therelay station 120 and the destination station/node 130 can be configuredto both transmit and receive. The source 110 sends signals to the relaystation 120, and the relay station 120 sends signals to the destination130. The signals sent from the source 110 to the relay station 120, andfrom the relay station 120 to the destination 130 may comprise multipleorthogonal carrier frequencies, such as in the case where OFDMmodulation is used.

The present embodiment includes only one relay station 120. An ASTCrelaying scheme is applied using orthogonal frequency divisionmultiplexing (OFDM) modulation at the source 110. ASTC encoding isapplied to individual carriers over two consecutive OFDM symbol periods.The relay station 120 receives the OFDM signal using the two antennae122, 124. It does simple analog processing (such as the sampling andstorage of discrete time signals) of the received signal and performscoding. This coding can for example be 2×2 Alamouti coding. The codedsignal is then transmitted to the destination node/station 130.

To avoid interference, the data transmission from the sourcenode/station 110 to destination node/station 130 takes place over twophases. The transmission cycle thus consists of two phases. In the firstphase, the source node/station 110 to relay station 120 link isactivated and the destination node/station 130 remains silent. In thesecond phase, the relay station 120 to destination node/station 130 linkis activated and the source node/station 110 remains silent.

Simulations of the present embodiment were conducted using 16 carriersin each OFDM symbol. This however does not limit the number of carriersto 16 and a skilled reader will understand that the number of carrierscan be varied.

Alternative embodiments may also apply the ASTC relaying schemes tosingle-carrier cyclic prefix (SC-CP) systems where the ASTC encoding isalso applied to individual symbols over two consecutive SC-CP blocks.

Alternative embodiments may also have more than two antennae at therelay station 120, in which case antenna selection can be adopted. Onlytwo antennas are selected to implement the proposed schemes based onpre-defined selection criteria, e.g., best product channel SNR, etc.

Alternative embodiments may also have multiple relay stations whererelay selection can be performed in which one relay station is selectedto implement the proposed schemes based on a pre-determined selectioncriteria, e.g., best product channel SNR, etc.

Alternative embodiments may also have multiple relay stations whereCoordinated Delay ASTC is implemented at each relay station, and thecoordinated delays are applied at different relay station. In this case,the delay durations applied at the different relay station is a designparameter obtained from a central control. This embodiment may have theadvantage that the carrier frequencies do not have to be orthogonal andthus signal collisions will not occur.

Alternative embodiments may also have only one antenna at the relaystation 120. In this case, a solution is to implement cooperation usingat least two relay sub-stations, where each relay sub-station is a relaystation capable of performing information passing with other relaysub-stations. Information passing is implemented between the at leasttwo relay sub-stations and the at least two relay sub-stations can thenparticipate in the ASTC transmission.

Angular Carrier Frequency Offset (ACFO)

Let the number of carriers be N. The source 110 to relay station 120 andrelay station 120 to destination 130 channels are assumed to befrequency selective multipath fading channels. Let the vectors h_(S,1)and h_(S,2) respectively denote the channel impulse response (CIR) fromthe source 110 to the first and second antennae 122, 124 of the relaystation 120. h_(S,1) and h_(S,2) both have the size of (L_(1×1)).Similarly, let the vectors h_(1,D) and h_(2,D) respectively denote theCIR from the first and second antennae 122, 124 of the relay station 120to the destination 130. h_(1,D) and h_(2,D) both have the size of(L_(2×1)). Let f₀, f_(r) and f_(d) be the carrier frequency of the localoscillators at the source 110, relay station 120 and destination 130,respectively. Then Δf_(r)=f₀−f_(r) and Δf_(d)=f₀−f_(d) respectivelydenote the CFO at the relay 120 and destination 130. The source 110,relay station 120 and destination 130 can have independent localoscillators and thus their oscillating frequency need not be the same.This results in independent CFOs in the signal received at relay station120 and the destination 130 i.e. Δf_(r)≠Δf_(d).

The angular CFO (ACFO) is defined as

$\varphi_{r} = {\frac{2\pi}{N}\left( {\Delta \; f_{r}} \right)T}$${\varphi_{d} = {\frac{2\pi}{N}\left( {\Delta \; f_{d}} \right)T}},$

where φ_(r) denotes the ACFO that is present at the channels between thesource 110 and either antenna 122, 124 of the relay station 120, andφ_(d) denotes the ACFO that is present at the channels between eitherantenna 122, 124 of the relay station 120 and the destination 130. Tdenotes the OFDM symbol duration. Scalars ε_(r)=(Δf_(r))T andε_(d)=(Δf_(d))T are referred to as normalized CFOs and their magnitudesare bounded by |ε_(r)|≦0.5 and |ε_(d)|≦0.5.

The ACFO φ_(r) and/or φ_(d) can be estimated during channel estimationand are used to perform compensation either at the relay station 120, orat the destination 130.

Joint ACFO compensation can also be performed at the destination 130, inwhich case no ACFO compensation needs to be done at the relay station120. What this means is that compensation for (φ_(r)+φ_(d)) is done atthe destination 130.

If the CFOs present in the signal received at the relay station 120 anddestination 130 are not properly compensated, then the gains due to therelaying and usage of OFDM modulation cannot be realized.

Joint ACFO compensation when done at the destination 130 is advantageousas it keeps the relay carrier frequency unaffected for anysource-and-destination pair.

Joint ACFO compensation when done at the destination 130 is alsoadvantageous as it simplifies the implementation of the relay station120 and reduces the computational complexity at the relay station 120.

Cyclic Prefix Schemes with Carrier Frequency Offset (CFO) Compensation

The embodiment employs two cyclic prefix schemes which are describedbelow with their associated methods of performing carrier frequencyoffset (CFO) compensation. The Cyclic Prefix Schemes 1 and 2 of thepresent invention permits the implementation of space-time codes withminimum signal processing complexity at the relay station.

It is understood that the term “CP Scheme 1” is also used in thisdocument to refer to the Cyclic Prefix Scheme 1 and “CP Scheme 2” isalso used to refer to the Cyclic Prefix Scheme 2.

Cyclic Prefix Scheme 1

FIG. 2 shows a scheme for inserting cyclic prefixes according to theexample embodiment. Let x_(j) be a (N×1) vector containing the N datasymbols to be transmitted during a j-th OFDM symbol duration.

While this example embodiment of the invention has been described using2 OFDM symbols i.e. x_(2n), and x_(2n+1), it is clear that the use of adifferent number of OFDM symbols is possible within the scope of theinvention, as will be clear to a skilled reader.

In step 202, the source derives a first cyclic prefix (denoted CP_(j,1))with length P₁=L₁−1 from x_(j). L₁ is the length of the channel impulseresponse (CIR) represented by h_(S,1) and h_(S,2) respectively for thechannel between the source and the first antenna of the relay station,and the channel between the source and the second antenna of the relaystation.

In step 204, the source inserts CP_(j,1) in front of x_(j) and thentransmits the resultant symbol sequence.

Let the symbol sequence x_(j) consisting of N symbols be denoted byx_(n) where n=0 . . . N−1, i.e.

x_(j)=[x₀ . . . x_(n) . . . x_(N-1])

The cyclic prefix CP_(j,1) of length P₁ is created by copying the lastP₁ symbols of x_(j)

CP_(j,1)=└x_(N-P) ₁ . . . x_(N-2) . . . x_(N-1┘)

The cyclic prefix CP_(j,1) is inserted in front of x_(j), producing theresultant symbol sequence └CP_(j,1) x_(j)┘ for transmission.

The transmission from the source to relay station takes place in thefirst phase of the transmission cycle.

In step 206, the relay station receives └CP_(j,1) x_(j)┘ at bothantennae of the station.

In step 208, after performing time synchronization, the CP_(j,1) portionof length P₁ in each OFDM symbol is removed leaving x_(j). Should ACFObe present, the signal vectors received over the span of 2 OFDM symboldurations i.e. for j={2n, 2n+1} are given after the removal of CP_(j,1)as

$\begin{bmatrix}r_{R,\; 1,\; {2\; n}} & r_{R,\; 1,\; {{2\; n}\; + \; 1}} \\r_{R,\; 2,\; {2\; n}} & r_{R,\; 2,\; {{2\; n}\; + \; 1}}\end{bmatrix} = {\quad {\quad{\quad{\left\lbrack \begin{matrix}{^{{j(\; {2\; {\; {n{({N\; + \; P_{1}})}}}\; P_{1}})}\; \varphi_{r}}\; {Z_{N}\left( \varphi_{r} \right)}\; H_{S,\; 1}\; W_{N}^{H}\; x_{2\; n}} & {^{{j(\; {{{({{2\; n}\; + \; 1})}\; {({N\; + \; P_{1}})}}\; + \; P_{1}})}\; \varphi_{r}}\; {Z_{N}\left( \varphi_{r} \right)}\; H_{S,\; 1}\; W_{N}^{H}\; x_{{2\; n}\; + \; 1}} \\{^{{j(\; {2\; {\; {n{({N\; + \; P_{1}})}}}\; P_{1}})}\; \varphi_{r}}\; {Z_{N}\left( \varphi_{r} \right)}\; H_{S,\; 2}\; W_{N}^{H}\; x_{2\; n}} & {^{{j(\; {{{({{2\; n}\; + \; 1})}\; {({N\; + \; P_{1}})}}\; + \; P_{1}})}\; \varphi_{r}}\; {Z_{N}\left( \varphi_{r} \right)}\; H_{S,\; 2}\; W_{N}^{H}\; x_{{2\; n}\; + \; 1}}\end{matrix} \right\rbrack + {\quad\begin{bmatrix}v_{R,\; 1,\; {2\; n}} & v_{R,\; 1,\; {{2\; n}\; + \; 1}} \\v_{R,\; 2,\; {2\; n}} & v_{R,\; 2,\; {{2\; n}\; + \; 1}}\end{bmatrix}}}}}}$

r_(R,i,j) denotes the received signal vector obtained after the removalof CP_(j,1), with i and j respectively denoting the antenna index andOFDM symbol duration. r_(R,i,j) has the size of (N×1). n denotes thedata transmission cycle index. The (N×N) matrix W_(N) ^(H) is theinverse discrete Fourier transform (IDFT) matrix. The first columnvector of the (N×N) circulant matrices h_(S,1) and H_(S,2) are [h_(S,1)^(T), 0_(1×(N-L))]^(T) and [h_(S,2) ^(T), 0_(1×(N-L))]^(T),respectively.

Vector v_(R,i,j) contains N samples of additive white Gaussian noise(AWGN) that distorts the signal received by the i-th relay antennaduring j-th OFDM symbol duration. If 2d OFDM symbols are transmitted ineach cycle with d being an integer value, then the matrix

$V = \begin{bmatrix}v_{R,1,{2n}} & v_{R,1,{{2n} + 1}} \\v_{R,2,{2n}} & v_{R,2,{{2n} + 1}}\end{bmatrix}$

will be of dimension (2N×2d) with OFDM symbol indexes of 2dn, 2dn+1,2dn+2, . . . , 2dn+2d−1.

It is assumed that the covariance of v_(R,i,j,)

E[v _(R,i,j) v _(R,i,j) ^(H)]=σ_(R) ² I _(N) for i=1,2 and j=2n,2n+1 ford>1.

Optionally, in the event that ACFO is present, compensation of ACFOφ_(r) can be performed at the relay station as step 230.

Assuming the complete removal of ACFO or if ACFO was absent, over thespan of 2 OFDM symbol durations i.e. for j={2n, 2n+1}, the receivedsignal vectors obtained after the removal of CP_(j,1) at the relay aregiven as follows:

$\begin{bmatrix}r_{R,\; 1,\; {2\; n}} & r_{R,\; 1,\; {{2\; n}\; + \; 1}} \\r_{R,\; 2,\; {2\; n}} & r_{R,\; 2,\; {{2\; n}\; + \; 1}}\end{bmatrix} = {\left\lbrack \begin{matrix}{H_{S,1}W_{N}^{H}x_{2n}} & {H_{S,1}W_{N}^{H}x_{{2n} + 1}} \\{H_{S,2}W_{N}^{H}x_{2n}} & {H_{S,2}W_{N}^{H}x_{{2n} + 1}}\end{matrix} \right\rbrack + {\quad{\begin{bmatrix}v_{R,1,{2n}} & v_{R,1,{{2n} + 1}} \\v_{R,2,{2n}} & v_{R,2,{{2n} + 1}}\end{bmatrix},}}}$

Step 209 is then performed at the relay station. In step 209, Simpleprocessing is performed in order to implement space-time coding at thecarrier level. The matrix Y_(R) is computed and arranged:

$Y_{R} = {\left\lbrack y_{{ij},R} \right\rbrack = {\begin{bmatrix}y_{11,R} & y_{12,R} \\y_{21,R} & y_{22,R}\end{bmatrix} = \begin{bmatrix}r_{R,1,{2n}} & r_{R,1,{{2n} + 1}} \\{\zeta \left( r_{R,2,{{2n} + 1}}^{*} \right)} & {- {\zeta \left( r_{R,2,{2n}}^{*} \right)}}\end{bmatrix}}}$

The space-time code implemented can for example be the Alamouti code.

Given that

H _(S,1) W _(N) ^(H) x _(j) =W _(N) ^(H)Λ_(S,1) x _(j) for j=2n, 2n+1and i=1, 2,

where Λ_(S,i) is a (N×N) sized diagonal matrix whose diagonal elementsare given by the N-point DFT of CIR h_(S,i) for i=1, 2, i.e.,Λ_(S,i)=√{square root over (N)}diag (W_(N)[h_(S,i) ^(T), 0_(1×(N-L) _(i)₎]^(T)), it can be shown that

${Y_{R} = {\begin{bmatrix}r_{R,1,{2n}} & r_{R,1,{{2n} + 1}} \\{\zeta \left( r_{R,2,{{2n} + 1}}^{*} \right)} & {- {\zeta \left( r_{R,2,{2n}}^{*} \right)}}\end{bmatrix} = {{\frac{1}{\sqrt{2}}\begin{bmatrix}{W_{N}^{H}\Lambda_{S,1}x_{2n}} & {W_{N}^{H}\Lambda_{S,1}x_{{2n} + 1}} \\{W_{N}^{H}{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{S,2}^{*}x_{{2n} + 1}^{*}} & {{- W_{N}^{H}}{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{S,2}^{*}x_{2n}^{*}}\end{bmatrix}} + {\overset{\sim}{V}}_{R,n}}}},$

where the (2N×2N) sized matrix {tilde over (V)}_(R,n) is given by

${\overset{\sim}{V}}_{R,n} = {\begin{bmatrix}v_{v,1,{2n}} & v_{R,1,{{2n} + 1}} \\{\zeta \left( v_{R,2,{{2n} + 1}}^{*} \right)} & {- {\zeta \left( v_{R,2,{2n}}^{*} \right)}}\end{bmatrix}.}$

Step 209 further comprises steps 210 and 212.

In step 210, for those elements of Y_(R) where no signal conjugation isneeded e.g.: for y_(11,R) and y_(12,R), nothing needs to be done.

In step 212, for those elements of Y_(R) where signal conjugation isneeded e.g.: for y_(21,R) and y_(22,R), the OFDM symbol sequence isreordered using a mapping function ζ(.):

ζ(a)=[a(N−1), a(N−2), . . . ,a(0)]^(T),

the (N×1) sized input vector a=[a(0), a(1), . . . , a(N−1)]^(T). Thisfunction can be easily implemented in hardware by storing the signalsamples in a shift register and then reading the register in reverseorder. This represents a significant advantage because reorderingoperations that are more complex than mere reversal, such as theinsertion, deletions and swapping of signal samples do not have to bedone.

It can be shown that

$\begin{matrix}{{\zeta \left( \left\lbrack {H_{S,i}W_{N}^{H}x_{j}} \right\rbrack^{*} \right)} = {\zeta \left( {H_{S,i}^{*}\left( {W_{N}^{H}x_{j}} \right)}^{*} \right)}} \\{= {{\zeta \left( H_{S,i}^{*} \right)}\left( {W_{N}^{H}x_{j}} \right)^{*}}} \\{= {W_{N}^{H}{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{S,i}^{*}{TW}_{N}W_{N}^{H}{Tx}_{j}^{*}}} \\{= {W_{N}^{H}{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{S,i}^{*}{TTx}_{j}^{*}}} \\{{= {W_{N}^{H}{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{S,i}^{*}x_{j}^{*}}}\mspace{11mu}}\end{matrix}$  for  j = 2n, 2n + 1  and  i = 1, 2,

where matrix Z_(N)(φ) denotes a (N×N) diagonal matrix given by

Z _(N)(φ)=diag([1,e ^(jφ) ,e ^(j2φ) , . . . ,e ^(j(N-1)φ)]^(T))

and T is a (N×N) permutation matrix such that

T=[ζ(I _(N))]⁽¹⁾ and TT=I _(N).

I_(N) is an identity matrix of size N. The operator [•]* represents acomplex conjugation.

The notation [a]^((l)) denotes the circular shifting of vector a by lelements, where

[a] ⁽²⁾ =[a(N−2),a(N−1),a(0),a(1), . . . ,a(N−3)]^(T).

For a given matrix X, matrix [X]^((l)) is obtained by circular shiftingeach column vector of X by l elements.

In step 213, a second cyclic prefix (denoted CP_(ij,2)) with length P₂where P₂=L₂−1 is obtained for each y_(ij,R). L₂ is the length of theCIRs denoted by the vectors h_(1,D) and h_(2,D) respectively for thechannel between the first antenna of the relay station and thedestination, and the channel between the second antenna of the relaystation and the destination. Each of the cyclic prefixes CP_(ij,2) isderived from the corresponding y_(ij,R.)

The cyclic prefixes CP_(ij,2) are then inserted in front of y_(ij,R) toproduce the symbol sequences └CP_(ij,2) y_(ij,R) ┘. It is to be notedthat y_(ij,R) is a (N×1) sized vector.

In step 214, the other necessary steps for the ASTC implementation atthe relay station are performed. The symbol sequences └CP_(ij,2)y_(ij,R) ┘ are then transmitted by the i-th relay antenna during thej-th OFDM symbol duration, where i=1, 2 and j={2n, 2n+1}. Thetransmission from the relay station to destination takes place in thesecond phase of the transmission cycle where the source remains silent.

In step 216, after frame synchronization, the destination removes thecyclic prefix of length P₂ from each OFDM symbol received. The OFDMsymbol with the cyclic prefix removed can be denoted by the (N×1) signalvector r_(D,j) for each j-th OFDM symbol duration.

Assuming that ACFO is present and ACFO compensation was done at therelay, for the j={2n, 2n+1}-th OFDM symbol duration, the (N×1) receivedsignal vectors at the destination in the presence of ACFO φ_(d) aregiven by

-   -   CP Scheme 1:

$r_{D,{2n}} = {{\frac{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2n}} + {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{{sn} + 1}^{*}}} \right\rbrack}} + p_{D,{2n}}}$${r_{D,{{2n} + 1}} = {{\frac{^{{j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2n} + 1}} - {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{sn}^{*}}} \right\rbrack}} + p_{D,{{2n} + 1}}}},$

where the noise vectors are given by

$p_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}v_{R,1,{2n}}} + {H_{2,D}{\zeta \left( v_{R,2,{{2n} + 1}}^{*} \right)}}} \right\rbrack}} + v_{D,{2\; n}}}$$p_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}v_{R,1,{{2n} + 1}}} - {H_{2,D}{\zeta \left( v_{R,2,{2n}}^{*} \right)}}} \right\rbrack}} + {v_{D,{{2\; n} + 1}}.}}$

Optionally, ACFO φ_(d) compensation can be performed at the destinationas step 240.

Assuming that ACFO is present and no ACFO compensation was done at therelay, for the j={2n, 2n+1}-th OFDM symbol duration,

$r_{D,{2\; n}} = {^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}{Z_{N}\left( \varphi_{d} \right)}{\quad{{\begin{bmatrix}{{^{{j{({{2\; {n{({N + P_{1}})}}} + P_{1}})}}\varphi_{r}}H_{1,D}{Z_{N}\left( \varphi_{r} \right)}W_{N}^{H}\Lambda_{S,1}x_{2\; n}} +} \\{^{{- {j{({{{({{2\; n} + 1})}{({N + P_{1}})}} + P_{1} + N - 1})}}}\varphi_{r}}H_{2,D}{Z_{N}\left( \varphi_{r} \right)}W_{N}^{H}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{{2\; n} + 1}^{*}}\end{bmatrix} + {p_{D,{2\; n}}r_{D,{{2\; n} + 1}}}} = {^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}{Z_{N}\left( \varphi_{d} \right)}{\quad{\left\lbrack \begin{matrix}{{^{{j{({{{({{2\; n} + 1})}{({N + P_{1}})}} + P_{1}})}}\varphi_{r}}H_{1,D}{Z_{N}\left( \varphi_{r} \right)}W_{N}^{H}\Lambda_{S,1}x_{{2\; n} + 1}} -} \\{^{{- {j{({{2\; {n{({N + P_{1}})}}} + P_{1} + N - 1})}}}\varphi_{r}}H_{2,D}{Z_{N}\left( \varphi_{r} \right)}W_{N}^{H}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{2\; n}^{*}}\end{matrix} \right\rbrack + {p_{D,{{2\; n} + 1}}.}}}}}}}$

H_(1,D) and H_(2,D) are (N×N) circulant matrices respectively with[h_(1,D) ^(T), 0_(1×(N-L))]^(T) and [h_(2,D) ^(T), 0_(1×(N-L))]^(T) astheir first column vectors. The (N×1) vector P_(D,2n) represent additivenoise.

Assuming that ACFO compensation was performed, or if ACFO is absent, forthe j=(2n)-th OFDM symbol duration

${r_{D,{2\; n}} = {{H_{1,D}W_{N}^{H}\Lambda_{S,1}x_{2\; n}} + {H_{2,D}W_{N}^{H}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{{2\; n} + 1}^{*}} + p_{D,{2\; n}}}},$

The (N×1) vector p_(D,2n) representing the additive noise is given by

P _(D,2n) =H _(1,D) v _(R,1,2n) +H _(2,D)ζ(v* _(R,2,2n+1))+V _(D,2n,)

where the (N×1) vector V_(D,2n) contains the N samples of AWGN atdestination with covariance matrix E[v_(D,2n)v_(D,2n) ^(H)]=σ_(D)²I_(N).

Similarly, for the j=(2n+1)-th OFDM symbol duration,

$r_{D,{{2\; n} + 1}} = {{H_{1,D}W_{N}^{H}\Lambda_{S,1}x_{{2\; n} + 1}} - {H_{2,D}W_{N}^{H}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{2\; n}^{*}} + p_{D,{{2\; n} + 1}}}$p_(D, 2 n + 1) = H_(1, D)v_(R, 1, 2 n + 1) − H_(2, D)ζ(v_(R, 2, 2 n)^(*)) + v_(D, 2n + 1).

In step 218, the destination performs ASTC decoding in the frequencydomain using the channel state information (CSI) parameters that wereobtained during training. N-point DFTs are performed on the signalvector r_(D,j) for the symbol durations j={2n, 2n+1}. Assuming that ACFOis absent, the N-point DFT of r_(D,2n) is

${W_{N}r_{D,{2\; n}}} = {{\Lambda_{1,D}\Lambda_{S,1}x_{2\; n}} + {\Lambda_{2,D}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{{2\; n} + 1}^{*}} + {W_{N}{p_{D,{2\; n}}.}}}$

Similarly, the N-point DFT of the signal vector received by thedestination during the (2n+1)-th OFDM symbol duration (i.e. r_(D,2n+1))is given by

${W_{N}r_{D,{{2\; n} + 1}}} = {{\Lambda_{1,D}\Lambda_{S,1}x_{{2\; n} + 1}} - {\Lambda_{2,D}{Z_{N}\left( \frac{2\; \pi}{N} \right)}\Lambda_{S,2}^{*}x_{2\; n}^{*}} + {W_{N}p_{D,{{2\; n} + 1}}}}$

A (2N×1) vector y_(D,n) is constructed as

$\begin{matrix}{y_{D,n} = \left\lbrack {\left( {W_{N}r_{D,{2n}}} \right)^{T},\left( {W_{N}r_{D,{{2n} + 1}}} \right)^{H}} \right\rbrack^{T}} \\{{= {{H_{P}\begin{bmatrix}x_{2n} \\x_{{2n} + 1}^{*}\end{bmatrix}} + \begin{bmatrix}{W_{N}p_{D,{2n}}} \\\left( {W_{N}p_{D,{{2n} + 1}}} \right)^{*}\end{bmatrix}}},}\end{matrix}$

Estimates of x_(2n) and x_(2n+1) (denoted {tilde over (x)}_(2n) {tildeover (x)}_(2n+1)) can be obtained using the conjugate transpose of H_(P)i.e. H_(P) ^(H)

$\begin{matrix}{\begin{bmatrix}{\overset{\sim}{x}}_{2n} \\{\overset{\sim}{x}}_{{2n} + 1}^{*}\end{bmatrix} = {H_{P}^{H}y_{D,n}}} \\{= {H_{P}^{N}\begin{bmatrix}{W_{N}r_{D,{2n}}} \\\left( {W_{N}r_{D,{{2n} + 1}}} \right)^{*}\end{bmatrix}}}\end{matrix}$

H_(P) is the (2N×2N) sized product channel matrix and is given by

$H_{P} = {\begin{bmatrix}{\Lambda_{1,D}\Lambda_{S,1}} & {{Z_{N}\left( \frac{2\pi}{N} \right)}\Lambda_{2,D}\Lambda_{S,2}^{*}} \\{{- {Z_{N}\left( {- \frac{2\pi}{N}} \right)}}\Lambda_{2,D}^{*}\Lambda_{S,2}} & {\Lambda_{1,D}^{*}\Lambda_{S,1}^{*}}\end{bmatrix}.}$

The product channel matrix H_(P) is a known parameter obtained duringthe product channel matrix estimation and forms part of the channelstate information (CSI). H_(P) allows for a simple linear decoding atdestination, since

H _(P) ^(H) H _(P) =I ₂

(|Λ_(1,D)|²|Λ_(S,1) ²|+|Λ_(2,D)|²|Λ_(S,2)|²)

where

denotes performing a Kronecker product.

In step 230, the relay station optionally performs ACFO φ_(r)compensation. The signal vectors r_(R,i,j) received over the span of 2OFDM symbol durations j={2n, 2n+1} for antennae i=1, 2 are:

$\begin{bmatrix}r_{R,1,{2n}} & r_{R,1,{{2n} + 1}} \\r_{R,2,{2n}} & r_{R,2,{{2n} + 1}}\end{bmatrix} = {\quad{\left\lbrack \begin{matrix}{^{{j{({{2{n{({N + P_{1}})}}} + P_{1}})}}\varphi_{r}}{Z_{N}\left( \varphi_{r} \right)}H_{S,1}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P_{1}})}} + P_{1}})}}\varphi_{r}}{Z_{N}\left( \varphi_{r} \right)}H_{S,1}W_{N}^{H}x_{{2n} + 1}} \\{^{{j{({{2{n{({N + P_{1}})}}} + P_{1}})}}\varphi_{r}}{Z_{N}\left( \varphi_{r} \right)}H_{S,2}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P_{1}})}} + P_{1}})}}\varphi_{r}}{Z_{N}\left( \varphi_{r} \right)}H_{S,2}W_{N}^{H}x_{{2n} + 1}}\end{matrix} \right\rbrack + {\quad{\begin{bmatrix}v_{R,1,{2n}} & v_{R,1,{{2n} + 1}} \\v_{R,2,{2n}} & v_{R,2,{{2n} + 1}}\end{bmatrix}.}}}}$

The ACFO φ_(r) is a known parameter obtained at the relay station duringthe ACFO {circumflex over (φ)}_(r), estimation step 410 and forms partof the channel state information (CSI).

The effect of the ACFO φ_(r) can be removed for r_(R,1,2n) andr_(R,2,2n) by multiplying r_(R,1,2n) and r_(R,2,2n) with the conjugateof e^(j(2n(N+P) ¹ ^()+P) ¹ ^()φ) ^(r) Z_(N)(φ_(r)). The effect of theACFO φ_(r) can be removed for r_(R,1,2n+1) and r_(R,2,2n+1) bymultiplying r_(R,1,2n+1) and r_(R,2,2n+1) with the conjugate ofe^(j((2n(N+P) ¹ ^()+P) ¹ ^()φ) ^(r) Z_(N)(φ_(r)).

In step 240, the destination optionally performs ACFO φ_(d)compensation. The (N×1) received signal vectors at the destination inthe presence of ACFO φ_(d) are given by

-   -   CP Scheme 1:

$r_{D,{2n}} = {{\frac{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2n}} + {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{{2n} + 1}^{*}}} \right\rbrack}} + p_{D,{2n}}}$${r_{D,{{2n} + 1}} = {{\frac{^{{j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2n} + 1}} - {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{2n}^{*}}} \right\rbrack}} + p_{D,{{2n} + 1}}}},$

where the noise vectors are given byp_(D,2n) and p_(D,2n+1). The ACFOφ_(d) is a known parameter obtained at the destination during the ACFO{circumflex over (φ)}_(d) _(—) estimation step 420 and forms part of thechannel state information (CSI).

The effect of the ACFO φ_(d) can be removed by multiplying r_(D,2n) andr_(D,2n+1) respectively with the conjugate of e^(j(2n(N+P) ² ^()+P) ²^()φ) ^(d) Z_(N)(φ_(d)) and e^(j((2n+1)(N+P) ² ^()+P) ² ^()φ) ^(d)Z_(N)(φ_(d)).

The Cyclic Prefix Scheme 1 may have the advantage that only analogdomain processing has to be done at the relay, and only linearprocessing has to be done for maximum likelihood decoding at thedestination.

Cyclic Prefix Scheme 2

FIG. 3 shows an alternative scheme for inserting cyclic prefixesaccording to the example embodiment. Let x_(j) be a (N×1) vectorcontaining the N data symbols to be transmitted during a j-th OFDMsymbol duration.

While this example embodiment of the invention has been described using2 OFDM symbols i.e. x_(2n) and x_(2n+1), it is clear that the use of adifferent number of OFDM symbols is possible within the scope of theinvention, as will be clear to a skilled reader.

In step 302, the source derives a first cyclic prefix (denoted CP_(j,1))with length P from x_(j), where P=P₁+P₂=L₁+L₂−2. L₁ is the length of thechannel impulse response (CIR) represented by h_(S,1) and h_(S,2)respectively for the channel between the source 110 and the firstantenna 122 of the relay station 120, and the channel between the source110 and the second antenna 124 of the relay station 120. L₂ is thelength of the CIRs denoted by the vectors h_(1,D) and h_(2,D)respectively for the channel between the first antenna 122 of the relaystation 120 and the destination 130, and the channel between the secondantenna 124 of the relay station 120 and the destination 130.

In step 304, the source inserts CP_(j,1) in front of x_(j) and thentransmits the resultant symbol sequence.

Let the symbol sequence x_(j) consist of N symbols be denoted by x_(n)where n=0 . . . N−1, i.e.

x_(j)=[x₀ . . . x_(n) . . . x_(N−1])

The cyclic prefix CP_(j,1) of length P₁ is created by copying the lastNcp words of x_(j)

CP_(j,1)=└x_(N-P) ₁ . . . x_(N-2) . . . x_(N-1┘)

The cyclic prefix CP_(j,1) is inserted in front of x_(j), producing theresultant symbol sequence └CP_(j,1) x_(j) ┘ for transmission.

The transmission from the source 110 to relay station 120 takes place inthe first phase of the transmission cycle.

In step 306; the relay station receives └CP_(j,1) x_(j)┘ at bothantennae of the station.

In step 308, after performing time synchronization, the first P₁ samplesof the CP_(j,1) portion of each OFDM symbol is removed, leaving asequence represented by └CP_(j,2) x_(j) ┘. The first P₁ samples of eachOFDM symbol are distorted by the ISI induced by the frequency selectivefading occurring at the source to relay channels. The resulting OFDMsymbol will then have (N+P₂) samples. Should ACFO be present, the signalvectors received over the span of 2 OFDM symbol durations i.e. forj={2n, 2n+1} are given after the removal of CP_(j,1) as

$\begin{bmatrix}{\overset{\sim}{r}}_{R,1,{2n}} & {\overset{\sim}{r}}_{R,1,{{2n} + 1}} \\{\overset{\sim}{r}}_{R,2,{2n}} & {\overset{\sim}{r}}_{R,2,{{2n} + 1}}\end{bmatrix} = {\quad{\left\lbrack \begin{matrix}{^{{j{({{2{n{({N + P})}}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P})}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{{2n} + 1}} \\{^{{j{({{2{n{({N + P})}}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P})}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{{2n} + 1}}\end{matrix} \right\rbrack + {\quad{\begin{bmatrix}{\overset{\sim}{v}}_{R,1,{2n}} & {\overset{\sim}{v}}_{R,1,{{2n} + 1}} \\{\overset{\sim}{v}}_{R,2,{2n}} & {\overset{\sim}{v}}_{R,2,{{2n} + 1}}\end{bmatrix}.}}}}$

{tilde over (r)}_(R,i,j) denotes the ((N+P₂)×1) received signal vectorobtained after the removal of P₁ samples, with i and j respectivelydenoting the antenna index and OFDM symbol duration. n denotes the datatransmission cycle index. The (N×N) matrix W_(N) ^(H) is the inversediscrete Fourier transform (IDFT) matrix. Matrix {tilde over (H)}_(S,1)for i=1, 2 is a ((N+P₂)×N) matrix given by

${{\overset{\sim}{H}}_{S,i} = \begin{bmatrix}{H_{S,i}\left( {{{N - P_{2} + 1}:N},:} \right)} \\H_{S,i}\end{bmatrix}},$

with H_(S,1) being a (N×N) circulant matrix with [h_(S,1) ^(T),0_(1×(N-L) ₁ ⁾]^(T) as its first column vector and H_(S,1)(N−P₂+1: N,:)denotes the last P₂ row vectors of H_(S,1.)

The vector {tilde over (v)}_(R,i,j) of size ((N+P₂)×1) contains the AWGNaffecting the signal {tilde over (r)}_(R,i,j). The covariance matrix ofthe noise vector {tilde over (v)}_(R,i,j) at the relay station is givenby

E{{tilde over (v)}_(R,i,j){tilde over (v)}_(R,i,j) ^(H)}=σ_(R) ²I_(N+P)₂

Optionally, in the event that ACFO is present, ACFO φ_(r) compensationcan be performed at the relay station as Step 330.

Assuming the complete removal of ACFO or if ACFO was absent, over thespan of 2 OFDM symbol durations i.e. for j={2n, 2n+1}, the receivedsignal vectors obtained after the removal of the first P₁ samples of theCP_(j,1) portion of each OFDM symbol are given as follows:

${\begin{bmatrix}{\overset{\sim}{r}}_{R,1,{2n}} & {\overset{\sim}{r}}_{R,1,{{2n} + 1}} \\{\overset{\sim}{r}}_{R,2,{2n}} & {\overset{\sim}{r}}_{R,2,{{2n} + 1}}\end{bmatrix} = {\begin{bmatrix}{{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{2\; n}} & {{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{{2\; n} + 1}} \\{{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{2\; n}} & {{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{{2\; n} + 1}}\end{bmatrix} + \begin{bmatrix}{\overset{\sim}{v}}_{R,1,{2\; n}} & {\overset{\sim}{v}}_{R,1,{{2\; n} + 1}} \\{\overset{\sim}{v}}_{R,2,{2\; n}} & {\overset{\sim}{v}}_{R,2,{{2\; n} + 1}}\end{bmatrix}}},$

Step 309 is then performed at the relay station. In step 309, processingis performed in order to implement space-time coding at the carrierlevel. The matrix Y_(R) is computed and arranged:

$Y_{R} = {\left\lbrack y_{{ij},R} \right\rbrack = {\begin{bmatrix}y_{11,R} & y_{12,R} \\y_{21,R} & y_{22,R}\end{bmatrix} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{\overset{\sim}{r}}_{R,1,{2n}} & {\overset{\sim}{r}}_{R,1,{{2n} + 1}} \\{\zeta \left( {\overset{\sim}{r}}_{R,2,{{2n} + 1}}^{*} \right)} & {- {\zeta \left( {\overset{\sim}{r}}_{R,2,{2n}}^{*} \right)}}\end{bmatrix}}}}$

The operator [•]* represents a complex conjugation. The space-time codeimplemented can for example be the Alamouti code.

Step 309 further comprises steps 310 and 312.

In step 310, for those elements of Y_(R) where no signal conjugation isneeded e.g.: for y_(11,R) and y_(12,R), nothing needs to be done.

In step 312, for those elements of Y_(R) where signal conjugation isneeded e.g.: for y_(21,R) and y_(22,R), the OFDM symbol sequence fromthe respective {tilde over (r)}_(R,i,j) is reordered using the mappingfunction ζ(.):

ζ(a)=[a(N−1),a(N−2), . . . ,a(0)]^(T),

the (N×1) input vector a=[a(0), a(1), . . . , a(N−1)]^(T). This functioncan be easily implemented in hardware by storing the signal samples in ashift register and then reading the register in reverse order.

The mapping function ζ(.) can thus be re-expressed as

ζ(a(n))=a(N−n−1)

where a(n) denotes the n-th symbol of the OFDM symbol sequence a. A timedomain signal conjugation is then performed on each reordered symbolζ(a(n)), for n=0 . . . N−1.

Let b=ζ(a). It can be shown that after signal conjugation is done,taking B={B(0) . . . B(k) . . . B(N−1)} to be the correspondingfrequency domain sequence of b

B*(k)W _(N) ^(k(N-P) ² ⁻¹⁾ =B*(k)W _(N) ^(−k(P) ² ⁺¹⁾

i.e., the phase-shifted conjugate sequence.

The following Discrete Fourier Transform (DFT) properties are present:

-   -   Linearity: ax(n)+by(n)+by(n)        aX(k)+bY(k);    -   Cyclic Shift x((n+m)_(N))        W_(N) ^(−km)X(k);    -   Symmetry x*((−n)_(N))        X*(k)        x(n) and y(n) to denote the time domain sequence, X(k) and Y(k)        their corresponding frequency domain sequence, N the DFT size,        and

$W_{N} = {{\exp \left( {{- j}\frac{2\; \pi}{N}} \right)}.}$

In step 314, the other necessary steps for the ASTC implementation atthe relay station are performed. The symbol sequences contained in

$Y_{R} = {\left\lbrack y_{{ij},R} \right\rbrack = \begin{bmatrix}y_{11,R} & y_{12,R} \\y_{21,R} & y_{22,R}\end{bmatrix}}$

are then transmitted by the i-th relay antenna during the j-th OFDMsymbol duration, where i=1,2 and j={2n, 2n+1}. The transmission from therelay station to destination takes place in the second phase of thetransmission cycle where the source remains silent.

In step 316, after frame synchronization, the destination removes thecyclic prefix of length P₂ from each OFDM symbol received. Each OFDMsymbol after cyclic prefix removal will be N samples long and can bedenoted by the signal vector r_(D,j) for each j-th OFDM symbol duration.

Assuming that ACFO is present and ACFO compensation was done at therelay, for the j={2n, 2n+1}-th OFDM symbol duration, the (N×1) receivedsignal vectors at the destination in the presence of ACFO φ_(d) aregiven by

-   -   CP Scheme 2:

$r_{D,{2n}} = {{\frac{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2n}} + {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{{2n} + 1}^{*}}} \right\rbrack}} + {\overset{\sim}{p}}_{D,{2n}}}$${r_{D,{{2n} + 1}} = {{\frac{^{{j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2n} + 1}} - {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{2n}^{*}}} \right\rbrack}} + {\overset{\sim}{p}}_{D,{{2n} + 1}}}},$

where the noise vectors are given by

${\overset{\sim}{p}}_{D,{2n}} = {{\frac{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{Z_{N}\left( \varphi_{d} \right)}{R_{cp}\left\lbrack {{U_{1,D}{\overset{\sim}{v}}_{R,1,{2n}}} + {U_{2,D}{\zeta \left( {\overset{\sim}{v}}_{R,2,{{2n} + 1}}^{*} \right)}}} \right\rbrack}} + v_{D,{2n}}}$${\overset{\sim}{p}}_{D,{{2n} + 1}} = {{\frac{^{{j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{Z_{N}\left( \varphi_{d} \right)}{R_{cp}\left\lbrack {{U_{1,D}{\overset{\sim}{v}}_{R,1,{{2n} + 1}}} - {H_{2,D}\left( {\overset{\sim}{v}}_{R,2,{2n}}^{*} \right)}} \right\rbrack}} + {v_{D,{{2n} + 1}}.}}$

Optionally, ACFO φ_(d) compensation can be performed at the destinationas step 340.

Assuming that ACFO is present and no ACFO compensation was done at therelay, for the j={2n, 2n+1}-th OFDM symbol duration,

r _(D,2n) =e ^(j(2n(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(N)(φ_(d)+φ_(r))[α_(n) {hacek over (H)} _(1,D) H _(S,1) W _(N) ^(H) x_(2n)γ_(n) {hacek over (H)} _(2,D) G _(S,2)(W _(N) ^(H) x_(2n+))*]+{tilde over (p)} _(D,2n)

r _(D,2n+1) =e ^(j((2n+1)(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(N)(φ_(d)+φ_(r))[α_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)} _(1,D) H_(S,1) W _(N) ^(H) x _(2n+1)−γ_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)}_(2,D) G _(S,2)(W _(N) ^(H) x _(2n))*]+{tilde over (p)} _(D,2n+1,)

where {hacek over (H)}_(1,D) and {hacek over (H)}_(2,D) are (N×N)circulant matrix with Z_(N)(−φ_(r)) [h_(1,D) ^(T), 0_(1×(N-L) ₂₎]^(T and Z) _(N)(−φ_(r)) [h_(2,D) ^(T), 0_(1×(N-L) ²⁾ ]^(T) as theirrespective first column vectors and scalars α_(n) and γ_(n) are definedas follows:

α_(n)=e^(j(2n+1)P) ¹ ^(φ) ^(r)

γ_(n)=e^(−j((4n+2)(N+P)−2nP) ¹ ^(-1)φ) ^(r.)

Optionally, joint ACFO compensation can be performed at the destinationas step 350 to compensate for the ACFO φ_(r) and φ_(d).

Assuming that ACFO compensation was performed, or if ACFO is absent, forthe j=(2n)-th OFDM symbol duration

r _(D,2n) =H _(1,D) H _(S,1) W _(N) ^(H) x _(2n) +H _(2,D) G _(S,2)(W_(N) ^(H) x _(2n+1))*+{tilde over (p)} _(D,2n,)

The (N×N) matrix G_(S,2) is given by

G _(S,2)=ζ({tilde over (H)}* _(S,2)(1:N,:)).

The mapping ζ(.) for a 2-dimensional matrix A is computed as follows:

Given that A has a size of (N₁×N₂) and A=[a₁, a₂, . . . , a_(N) ₂ ]where a_(i) is (N_(1×1)) vector for i=1, 2, . . . , N₂, thenζ(A)=[ζ(a₁), ζ(a₂), . . . , ζ(a_(N) ₂ )].

The (N×1) vector {tilde over (p)}_(D,2n) is given by

{tilde over (p)} _(D,2n) =R _(cp) [U _(1,D) {tilde over (v)} _(R,1,2n)+U _(2,D)ζ({tilde over (v)} _(R,2,2n+1))]v _(D,2n,)

where vector v_(D,2n) contains the AWGN received at the destination fori=1, 2, the matrix U_(1,D) is a ((N+P₂)×(N+P₂)) Toeplitz matrix with[h_(1,D) ^(T), 0_(1×(N+P) ₂ _(−L) ₂ ₎]^(T) as its first column vectorand [h_(1,D)(1, 1), 0_(1×(N+P) ₂ ⁻¹⁾] as its first row vector. MatrixR_(cp) is a (N×(N+P₂)) matrix defined as

R_(cp)=[0_(N×P) ₂ ,I_(N)].

Similarly, the (N×1) sized signal vector received at the destinationduring (2n+1)th OFDM symbol duration is obtained to be

r _(D,2n+1) =H _(1,D) H _(S,1) W _(N) ^(H) x _(2n+1) −H _(2,D) G_(S,2)(W _(N) ^(H) x _(2n))*+{tilde over (p)} _(D,2n+1,)

{tilde over (p)} _(D,2n+1) =R _(cp) [U _(1,D) {tilde over (v)}R,1,2n+1U_(2,D)ζ({tilde over (v)}* _(R,2,2n))]+v _(D,2n+.)

In step 318, the destination performs the ASTC decoding in the frequencydomain using the channel state information (CSI) parameters that wereobtained during training. N-point DFTs are performed on the signalvector r_(D,j) for the symbol durations j={2n, 2n+1}, resulting in thevectors W_(N)r_(D,2n) and W_(N)r_(D,2n+1)

A (2N×1) vector y_(D,n) is constructed as

$\begin{matrix}{y_{D,n} = \left\lbrack {\left( {W_{N}r_{D,{2n}}} \right)^{T},\left( {W_{N}r_{D,{{2n} + 1}}} \right)^{H}} \right\rbrack^{T}} \\{= {{H_{P}\begin{bmatrix}x_{2n} \\x_{{2n} + 1}^{*}\end{bmatrix}} + \begin{bmatrix}{W_{N}{\overset{\sim}{p}}_{D,{2n}}} \\\left( {W_{N}{\overset{\sim}{p}}_{D,{{2n} + 1}}} \right)^{*}\end{bmatrix}}}\end{matrix}$

The signals r_(D,2n) and r_(D,2n+1) can be represented as

r _(D,2n) =H _(1,D) H _(S,1) W _(N) ^(H) x _(2n) +H _(2,D) G _(S,2)(W_(N) ^(H) x _(2n+1))*+{tilde over (p)} _(D,2n,)

r _(D,2n+1) =H _(1,D) H _(S,1) W _(N) ^(H) x _(2n+1) −H _(2,D) G_(S,2)(W _(N) ^(H) x _(2n))*{tilde over (p)} _(D,2n+1,)

The matrix G_(S,2) is defined to be a (N×N) matrix of the form:

G _(S,2)=ζ({tilde over (H)}* _(S,2)(1:N,:)).

It can be observed that matrix G_(S,2) can be obtained by permutatingthe column vectors of a (N×N) circulant matrix C_(S,2)=W_(N) ^(H)Λ^(*)_(S,2)W_(N). Using this knowledge, it can be shown that

$G_{S,2} = {{W_{N}^{H}\left\lbrack {\left( {Z_{N}\left( \frac{2\pi}{N} \right)} \right)^{L_{2}}\Lambda_{S,2}^{*}T} \right\rbrack}{W_{N}.}}$

Substituting G_(S,2) in the (N×1)-sized vector H_(2,D)G_(S,2)(W_(N)^(H)x_(2n+1))*,

$\begin{matrix}\begin{matrix}{{H_{2,D}{G_{S,2}\left( {W_{N}^{H}x_{{2n} + 1}} \right)}^{*}} = {W_{N}^{H}{\Lambda_{2,D}\left( {W_{N}G_{S,2}W_{N}^{H}} \right)}{W_{N}\left( {W_{N}^{H}x_{{2n} + 1}} \right)}^{*}}} \\{= {W_{N}^{H}{\Lambda_{2,D}\left( {\left( {Z_{N}\left( \frac{2}{N} \right)} \right)^{L_{2}}\Lambda_{S,2}^{*}T} \right)}{W_{N}\left( {W_{N}^{H}x_{{2n} + 1}} \right)}^{*}}} \\{= {W_{N}^{H}{\Lambda_{2,D}\left( {Z_{N}\left( \frac{2}{N} \right)} \right)}^{L_{2}}\Lambda_{S,2}^{*}T\; T\; x_{{2n} + 1}^{*}}} \\{= {{W_{N}^{H}\left( {Z_{N}\left( \frac{2}{N} \right)} \right)}^{L_{2}}\Lambda_{2,D}\Lambda_{S,2}^{*}\; x_{{2n} + 1}^{*}}}\end{matrix} \\{{{since}\mspace{14mu} T\; T} = {I_{N}.}}\end{matrix}$

Similarly, the (N×1) vector H_(2,D)G_(S,2)(W_(N) ^(H)x_(2n))* can beexpressed as

${H_{2,D}{G_{S,2}\left( {W_{N}^{H}x_{2n}} \right)}^{*}} = {{W_{N}^{H}\left( {Z_{N}\left( \frac{2}{N} \right)} \right)}^{L_{2}}\Lambda_{2,D}\Lambda_{S,2}^{*}\; {x_{2n}^{*}.}}$

Substituting the expressions of H_(2,D)G_(S,2)(W_(N) ^(H)x_(2n+1))* andH_(2,D)G_(S,2)(W_(N) ^(H)x_(2n))* into y_(D,n),

$\begin{matrix}{y_{D,n} = \left\lbrack {\left( {W_{N}r_{D,{2n}}} \right)^{T},\left( {W_{N}r_{D,{{2n} + 1}}} \right)^{H}} \right\rbrack^{T}} \\{= {{\begin{bmatrix}{\Lambda_{1,D}\Lambda_{S,1}} & {\left( {Z_{N}\left( \frac{2\pi}{N} \right)} \right)^{L_{2}}\Lambda_{2,D}\Lambda_{S,2}^{*}} \\{{- \left( {Z_{N}\left( {- \frac{2\pi}{N}} \right)} \right)^{L_{2}}}\Lambda_{2,D}^{*}\Lambda_{S,2}} & {\Lambda_{1,D}^{*}\Lambda_{S,1}^{*}}\end{bmatrix}\begin{bmatrix}x_{2\; n} \\x_{{2\; n} + 1}^{*}\end{bmatrix}} +}} \\{{\begin{bmatrix}{W_{N}p_{D,{2\; n}}} \\\left( {W_{N}p_{D,{{2\; n} + 1}}} \right)^{*}\end{bmatrix}.}}\end{matrix}$

Estimates of x_(2n) and x_(2n+1) (denoted {tilde over (x)}_(2n) and{tilde over (x)}*_(2n+1)) can be obtained using the conjugate transposeof H_(P) i.e. H_(P) ^(H)

$\begin{matrix}{\begin{bmatrix}{\overset{\sim}{x}}_{2n} \\{\overset{\sim}{x}}_{{2n} + 1}^{*}\end{bmatrix} = {H_{P}^{H}y_{D,n}}} \\{= {H_{P}^{N}\begin{bmatrix}{W_{N}r_{D,{2n}}} \\\left( {W_{N}r_{D,{{2n} + 1}}} \right)^{*}\end{bmatrix}}}\end{matrix}$

H_(P) is the (2N×2N) sized product channel matrix and is given by

$H_{P} = \begin{bmatrix}{\Lambda_{1,D}\Lambda_{S,1}} & {\left( {Z_{N}\left( \frac{2\pi}{N} \right)} \right)^{L_{2}}\Lambda_{2,D}\Lambda_{S,2}^{*}} \\{{- \left( {Z_{N}\left( {- \frac{2\pi}{N}} \right)} \right)^{L_{2}}}\Lambda_{2,D}^{*}\Lambda_{S,2}} & {\Lambda_{1,D}^{*}\Lambda_{S,1}^{*}}\end{bmatrix}$

The product channel matrix H_(P) is a known parameter obtained duringthe product channel matrix estimation and forms part of the channelstate information (CSI). H_(P) allows for a simple linear decoding atdestination, since

H _(P) ^(H) H _(P) =I ₂

(|Λ_(1,D)|²|Λ_(S,1)|²|Λ_(2,D)|²|Λ_(S,2)|²).

where

denotes performing a Kronecker product.

It can be seen that the present embodiment has an advantage in thatthere is no need for any sample reordering to be done at thedestination.

In the event that ACFO is present and joint ACFO compensation was donein step 316, the ASTC decoding in the frequency domain can be performedusing step 320 instead of step 318.

In step 320, the (2N×1) vector y_(D,n) will be

$\begin{matrix}{y_{D,n} = \begin{bmatrix}{\left( {^{{- {j{({{2{n{({N + P_{2}})}}} + P_{2}})}}}{(\varphi_{f})}}W_{N}{Z_{N}^{H}\left( \varphi_{f} \right)}r_{D,{2n}}} \right)^{T},} \\\left( {^{{- {j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}}{(\varphi_{f})}}W_{N}{Z_{N}^{H}\left( \varphi_{f} \right)}r_{D,{{2n} + 1}}} \right)^{H}\end{bmatrix}^{T}} \\{= {{\underset{{\overset{\sim}{H}}_{F}}{\underset{}{\begin{bmatrix}{\alpha_{n}{\overset{\Cup}{\Lambda}}_{1,D}\Lambda_{S,1}} & {{\gamma_{n}\left( {Z_{N}\left( \frac{2\pi}{N} \right)} \right)}^{L_{2}}{\overset{\Cup}{\Lambda}}_{2,D}\Lambda_{S,2}^{*}} \\{{- \gamma_{n}^{*}}{^{{- j}\; P_{1}\varphi_{r}}\left( {Z_{N}\left( {- \frac{2\pi}{N}} \right)} \right)}^{L_{2}}{\overset{\Cup}{\Lambda}}_{2,D}^{*}\Lambda_{S,2}} & {\alpha_{n}^{*}^{{- j}\; P_{1}\varphi_{r}}{\overset{\Cup}{\Lambda}}_{1,D}^{*}\Lambda_{S,1}^{*}}\end{bmatrix}}}\begin{bmatrix}x_{2n} \\x_{{2n} + 1}^{*}\end{bmatrix}} +}} \\{\underset{a_{n}}{\underset{}{\begin{bmatrix}{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}{(\varphi_{f})}}W_{N}{Z_{N}^{H}\left( \varphi_{f} \right)}{\overset{\sim}{p}}_{D,{2n}}} \\{^{{- {j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}}{(\varphi_{f})}}W_{N}{Z_{N}^{H}\left( \varphi_{f} \right)}{\overset{\sim}{p}}_{D,{{2n} + 1}}}\end{bmatrix}}}}\end{matrix}$ $y_{D,n} = {{{\overset{\sim}{H}}_{F}\begin{bmatrix}x_{2n} \\x_{{2n} + 1}^{*}\end{bmatrix}} + a_{n}}$

The scalars α_(n) and γ_(n) are defined as:

α_(n)=e^(j(2n+1)P) ¹ ^(φ) ^(r)

γ_(n)=e^(−j((4n+2)(N+P)−2nP) ¹ ^(−1)φ) ^(r.)

where φ_(r) represents the ACFO φ_(r). The value of φ_(r) can beestimated at the relay using the ACFO {circumflex over (φ)}_(r)estimation step 410 and then forwarded to the destination.

Estimates of x_(2n) and x_(2n+1) (denoted {tilde over (x)}_(2n) and{tilde over (x)}*_(2n+1)) can thus be obtained using {tilde over(H)}_(F) such that

$\begin{bmatrix}{\overset{\sim}{x}}_{2n} \\{\overset{\sim}{x}}_{{2n} + 1}^{*}\end{bmatrix} = {{\overset{\sim}{H}}_{F}^{H}{y_{D,n}.}}$

{tilde over (H)}_(F) ^(H) represents the conjugate transpose of {tildeover (H)}_(F). {tilde over (H)}_(F) has the property that

{tilde over (H)} _(F) ^(H) {tilde over (H)} _(F) =I ₂

(|{hacek over (Λ)}_(1,D)|²|Λ_(S,1)|²+|{hacek over(Λ)}_(2,D)|²|Λ_(S,2)|²).

where

denotes performing a Kronecker product. {tilde over (H)}_(F) thus allowsfor a simple linear decoding at the destination.

In step 330, the relay station optionally performs ACFO φ_(r)compensation. The signal vectors {tilde over (r)}_(R,i,j) received overthe span of 2 OFDM symbol durations j={2n,2n+1} for antennae i=1, 2 are:

$\begin{bmatrix}{\overset{\sim}{r}}_{R,1,{2n}} & {\overset{\sim}{r}}_{R,1,{{2n} + 1}} \\{\overset{\sim}{r}}_{R,2,{2n}} & {\overset{\sim}{r}}_{R,2,{{2n} + 1}}\end{bmatrix} = {\quad{\left\lbrack \begin{matrix}{^{{j{({{2{n{({N + P})}}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P})}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,1}W_{N}^{H}x_{{2n} + 1}} \\{^{{j{({{2{n{({N + P})}}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{2n}} & {^{{j{({{{({{2n} + 1})}{({N + P})}} + P_{1}})}}\varphi_{r}}{Z_{N + P_{2}}\left( \varphi_{r} \right)}{\overset{\sim}{H}}_{S,2}W_{N}^{H}x_{{2n} + 1}}\end{matrix} \right\rbrack + {\begin{bmatrix}{\overset{\sim}{v}}_{R,1,{2n}} & {\overset{\sim}{v}}_{R,1,{{2n} + 1}} \\{\overset{\sim}{v}}_{R,2,{2n}} & {\overset{\sim}{v}}_{R,2,{{2n} + 1}}\end{bmatrix}.}}}$

The ACFO φ_(r) is a known parameter obtained at the relay station duringthe ACFO {circumflex over (φ)}_(r) estimation step 410 and forms part ofthe channel state information (CSI).

The effect of the ACFO φ_(r) can be removed for {tilde over(r)}_(R,1,2n) and {tilde over (r)}_(R,2,2n) by multiplying with theconjugate of e^(j(2n(N+P) ¹ ^()+P) ¹ ^()φ) ^(r) Z_(N)(φ_(r)). The effectof the ACFO φ_(r) can be removed for {tilde over (r)}_(R,1,2n+1) and{tilde over (r)}_(R,2,2n+1) by multiplying with the conjugate ofe^(j((2n+1)(N+P) ¹ ^()+P) ¹ ^()φ) ^(r) Z_(N)(φ_(r)).

In step 340, the destination optionally performs ACFO φ_(d)compensation. The (N×1) received signal vectors at the destination inthe presence of ACFO φ_(d) are given by

-   -   CP Scheme 2:

$r_{D,{2n}} = {{\frac{^{{j{({{2{n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2n}} + {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{{2n} + 1}^{*}}} \right\rbrack}} + {\overset{\sim}{p}}_{D,{2n}}}$${r_{D,{{2n} + 1}} = {{\frac{^{{j{({{{({{2n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2n} + 1}} - {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{2n}^{*}}} \right\rbrack}} + {\overset{\sim}{p}}_{D,{{2n} + 1}}}},$

where the noise vectors are given by {tilde over (p)}_(D,2n) and {tildeover (p)}_(D,2n+1). The ACFO φ_(d) is a known parameter obtained duringthe ACFO {circumflex over (φ)}_(d) estimation step 420 and forms part ofthe channel state information (CSI).

The effect of the ACFO φ_(d) can be removed by multiplying r_(D,2n) andr_(D,2n+1) respectively with the conjugate of e^(j(2n(N+P) ² ^()+P) ²^()φ) ^(d) Z_(N)(φ_(d)) and e^(j((2n+1)(N+P) ² ^()+P) ² ^()φ) ^(d)Z_(N)(φ_(d)).

In step 350, the destination optionally performs joint ACFOcompensation. The (N×1) signal vectors received at the destination forthe j={2n, 2n+1}-th OFDM symbol duration are given by

r _(D,2n) =e ^(j(2n(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(N)(φ_(d)+φ_(r))[α_(n) {hacek over (H)} _(1,D) H _(S,1) W _(N) ^(H) x_(2n)+γ_(n) {hacek over (H)} _(2,D) G _(S,2)(W _(N) ^(H) x _(2n+1))*]

r _(D,2n+1) =e ^(j((2n+1)(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(N)(φ_(d)+φ_(r))[α_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)} _(1,D) H_(S,1) W _(N) ^(H) x _(2n+1)−γ_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)}_(2,D) G _(S,2)(W _(N) ^(H) x _(2n))*]+{tilde over (p)} _(D,2n+1,)

where the noise vectors are given by {tilde over (p)}_(D,2n) and {tildeover (p)}_(D,2n+1.)

The scalars α_(n) and γ_(n) are defined as follows:

α_(n)=e^(j(2n+1)P) ¹ ^(φ) ^(r)

γ_(n)=e^(−j((4n+2)(N+P)−2nP) ¹ ^(-1)φ) ^(r.)

It can be seen that ACFO φ_(r) and ACFO φ_(d) are present in the signalvectors r_(D,2n) and r_(D,2n+1). ACFO φ_(r) and ACFO φ_(d) can be addedtogether and be represented by ACFO φ_(f) i.e. φ_(f)=φ_(d)+φ_(r). TheACFO φ_(f) is a known parameter obtained during the joint ACFO(φ_(r)+φ_(d)) estimation step 430 and forms part of the channel stateinformation (CSI).

The effect of the ACFO φ_(f) can be removed by multiplying r_(D,2n) andr_(D,2n+1) respectively with the conjugates of e^(j(2n(N+P) ² ^()+P) ²^()(φ) ^(d) ^(+φ) ^(r) ⁾Z_(N)(φ_(d)+φ_(r)) and e^(j((2n+1)(N+P) ² ^()+P)² ^()(φ) ^(d) ^(+φ) ^(r) ⁾Z_(N)(φ_(d)+φ_(r)).

The Cyclic Prefix Scheme 2 may have the advantage that only analogdomain processing has to be done at the relay, and only linearprocessing has to be done for maximum likelihood decoding at thedestination for each carrier.

The Cyclic Prefix Scheme 2 may also be advantageous over the prior artbecause the relay station does not have to perform time sharing betweendifferent sources and destinations. In the prior art, the relay stationwill need to estimate and compensate the ACFO for eachsource-and-destination pair as joint ACFO compensation at thedestination is not done. This can complicate the relay station hardwareand could increase the computational complexity required at the relaystation.

Channel Estimation

Channel estimation is performed before actual information is transmittedaccording to the method shown in the flow-chart of FIG. 2 or FIG. 3. Thepurpose of channel estimation is to obtain a set of Channel StateInformation (CSI) parameters for use in decoding the signals received atthe destination and optionally to compensate for Angular CarrierFrequency Offset (ACFO) at either the relay station or the destination.

Channel estimation according to the example embodiment will be describednext with reference to FIG. 4.

In step 402, a simple pair of pilot symbols (or training symbols) isused to estimate the product channel. The pair of pilot symbolscomprising of

[x_(2n)x_(2n+1])

is transmitted over two symbol intervals from the source. The pilotsymbols are defined as

x_(2n)=a

X _(2n+1) =−a

where a is a (N×1) vector such that |a(i)|=1 for i=0, 1, . . . , N−1 anda has low peak to average power ratio (PAPR). n denotes the datatransmission cycle index.

ACFO {circumflex over (φ)}_(r) Estimation at the Relay Station

In step 410, ACFO {circumflex over (φ)}_(r) estimation is performed atthe relay station for either of Cyclic Prefix Schemes 1 or 2. Given theknown values of the pilot symbols [x_(2n) x_(2n+1)], the ACFO at therelay {circumflex over (φ)}_(r) can be easily estimated as

CP  Scheme  1:${\hat{\varphi}}_{r} = \frac{{\angle \left( {{- r_{R,1,{2n}}^{H}}r_{R,1,{{2n} + 1}}} \right)} + {\angle \left( {{- r_{R,2,{2n}}^{H}}r_{R,2,{{2n} + 1}}} \right)}}{2\left( {N + P} \right)}$CP  Scheme  2:${\hat{\varphi}}_{r} = {\frac{{\angle \left( {{- {\overset{\sim}{r}}_{R,1,{2n}}^{H}}{\overset{\sim}{r}}_{R,1,{{2n} + 1}}} \right)} + {\angle \left( {{- {\overset{\sim}{r}}_{R,2,{2n}}^{H}}{\overset{\sim}{r}}_{R,2,{{2n} + 1}}} \right)}}{2\left( {N + P} \right)}.}$

The operator ∠(.) returns the phase of (.) and hence the returned scalaris within the interval [−π,π). It is to be noted that

${\hat{\varphi}}_{r} = \frac{2{\pi\varepsilon}_{r}}{N}$

and hence the maximum normalized CFO that can be estimated is given bythe bounds

${{\hat{\varepsilon}}_{r}} \leq {0.5\frac{N}{N + P}} < 0.5$

The above limitation can be overcome by designing suitable pilotsymbols. The estimated ACFO value {circumflex over (φ)}_(r) can be usedby the relay to do the compensation during the transmission of actualinformation.

Cyclic Prefix Scheme 2 may have the advantage that ACFO compensation atrelay is not necessary because joint ACFO compensation can be performedat the destination.

ACFO {circumflex over (φ)}_(d) Estimation at the Destination

In step 420, ACFO {circumflex over (φ)}_(d) estimation is performed atthe destination station for either of Cyclic Prefix Schemes 1 or 2.

For Cyclic Prefix Scheme 1, the (N×1) received signal vectors at thedestination in the presence of ACFO φ_(d) are given by

-   -   CP Scheme 1

$r_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2\; n}} + {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{{2\; n} + 1}^{*}}} \right\rbrack}} + p_{D,{2\; n}}}$${r_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2\; n} + 1}} - {H_{2,D}{\zeta \left( H_{S,2}^{*} \right)}W_{N}^{H}{Tx}_{2\; n}^{*}}} \right\rbrack}} + p_{D,{{2\; n} + 1}}}},$

where the noise vectors are given by

$p_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}v_{R,1,{2\; n}}} + {H_{2,D}{\zeta \left( v_{R,2,{{2\; n} + 1}}^{*} \right)}}} \right\rbrack}} + v_{D,{2\; n}}}$$p_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}v_{R,1,{{2\; n} + 1}}} - {H_{2,D}{\zeta \left( v_{R,2,{2\; n}}^{*} \right)}}} \right\rbrack}} + {v_{D,{{2\; n} + 1}}.}}$

Similarly, the (N×1) received signal vectors at the destination for CPScheme 2 are given by

-   -   CP Scheme 2:

$r_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{2\; n}} + {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{{2\; n} + 1}^{*}}} \right\rbrack}} + p_{D,{2\; n}}}$${r_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{H_{1,D}H_{S,1}W_{N}^{H}x_{{2\; n} + 1}} - {H_{2,D}G_{S,2}W_{N}^{H}{Tx}_{2\; n}^{*}}} \right\rbrack}} + p_{D,{{2\; n} + 1}}}},$

where the noise vectors are given by

${\overset{\sim}{p}}_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{Z_{N}\left( \varphi_{d} \right)}{R_{cp}\left\lbrack {{U_{1,D}{\overset{\sim}{v}}_{R,1,{2\; n}}} + {U_{2,D}{\zeta \left( {\overset{\sim}{v}}_{R,2,{{2\; n} + 1}}^{*} \right)}}} \right\rbrack}} + v_{D,{2\; n}}}$${\overset{\sim}{p}}_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{Z_{N}\left( \varphi_{d} \right)}{R_{cp}\left\lbrack {{U_{1,D}{\overset{\sim}{v}}_{R,1,{{2\; n} + 1}}} - {H_{2,D}{\zeta \left( {\overset{\sim}{v}}_{R,2,{2\; n}}^{*} \right)}}} \right\rbrack}} + {v_{D,{{2\; n} + 1}}.}}$

The following estimation applies for either of Cyclic Prefix Schemes 1or 2. Using the pilot symbols of x_(2n)=a and x_(2n)=−a that weretransmitted by the source, it is assumed that W_(N) ^(H)a=b. The (N×N)matrix W_(N) ^(H) is the inverse discrete Fourier transform (IDFT)matrix. Therefore, vector H_(1,D)H_(S,1)W_(N) ^(H)x_(2n) can beexpressed as

$\begin{matrix}{{H_{1,D}H_{S,1}W_{N}^{H}x_{2n}} = {H_{1,D}H_{S,1}b}} \\{{= {A\; h_{P}}},}\end{matrix}$

where the (N×(P+1)) Toeplitz matrix A is given by

A=[[b ]⁽⁰⁾,[b]⁽¹⁾, . . . ,[b]^((P)])

and the ((P+1)×1) vector hp is

h _(P) =h _(1,D) *h _(S,1)

with * denoting convolution operation. Let us assume that d=W_(N)^(H)Ta*.

Vector H_(2,D) ζ(H*_(S,2))d can be written as

H _(2,D)ζ(H* _(S,2))d=B{tilde over (h)} _(P),

where the (N×(P+1)) Toeplitz matrix B is given by

B=[[f]^((−L) ¹ ⁺¹⁾,[f](−L ¹ ⁺²⁾, . . . ,[f]^((−L) ¹ ^(+P+1)])

with f=ζ(d) and the ((P+1)×1) vector {tilde over (h)}_(P) is

{tilde over (h)} _(P) =h _(2,D)*ζ(h* _(S,2)).

Similarly, vector H_(2,D)G_(S,2)d can be expressed as

H_(2,D)G_(S,2)d=C{tilde over (h)}_(P),

where the (N×(P+1)) Toeplitz matrix C is given by

c=[[f]^((−2L) ² ⁺¹⁾,[f]^((−2L) ² ⁺²⁾, . . . ,[f]^((−2L) ² ^(+P+1)].)

Substituting the above results into r_(D,2n) and r_(D,2n+1) and bearingin mind that r_(D,2n) and r_(D,2n+1) are the received signal vectors ofthe pilot symbols at the destination, r_(D,2n) and r_(D,2n+1) can berewritten as

-   -   CP Scheme 1:

$r_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {A,B} \right\rbrack}h_{F}} + p_{D,{2\; n}}}$$r_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{- A},{- B}} \right\rbrack}h_{F}} + p_{D,{{2\; n} + 1}}}$

-   -   CP Scheme 2:

$r_{D,{2\; n}} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {A,C} \right\rbrack}h_{F}} + {\overset{\sim}{p}}_{D,{2\; n}}}$${r_{D,{{2\; n} + 1}} = {{\frac{^{{j{({{{({{2\; n} + 1})}{({N + P_{2}})}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}{{Z_{N}\left( \varphi_{d} \right)}\left\lbrack {{- A},{- C}} \right\rbrack}h_{F}} + {\overset{\sim}{p}}_{D,{{2\; n} + 1}}}},$

where the (2(P+1)×1) vector h_(F)

h_(F)=[h_(P) ^(T), {tilde over (h)}_(P) ^(T)]^(T).

Let q_(n) be a (2N×1) vector constructed as

$\begin{matrix}{q_{n} = \left\lbrack {r_{D,{2n}}^{T},r_{D,{{2n} + 1}}^{T}} \right\rbrack^{T}} \\{{= {{{F\left( \varphi_{d} \right)}h_{F}} + e_{n}}},}\end{matrix}$

where e_(n)=[p_(D,2n) ^(T), p_(D,2n+1) ^(T)]^(T) for CP Scheme 1 ande_(n)=[{tilde over (p)}_(D,2n) ^(T), {tilde over (p)}_(D,2n+1) ^(T)]^(T)for CP Scheme 2. The (2N×2(P+1)) matrix F(φ_(d)) is given by

-   -   CP Scheme 1

${F\left( \varphi_{d} \right)} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}\begin{bmatrix}{Z_{N}\left( \varphi_{d} \right)} & 0_{N \times N} \\0_{N \times N} & {^{{j{({N + P_{2}})}}\varphi_{d}}{Z_{N}\left( \varphi_{d} \right)}}\end{bmatrix}}\begin{bmatrix}A & {- B} \\{- A} & {- B}\end{bmatrix}}$

-   -   CP Scheme 2

${F\left( \varphi_{d} \right)} = {{{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{d}}}{\sqrt{2}}\begin{bmatrix}{Z_{N}\left( \varphi_{d} \right)} & 0_{N \times N} \\0_{N \times N} & {^{{j{({N + P_{2}})}}\varphi_{d}}{Z_{N}\left( \varphi_{d} \right)}}\end{bmatrix}}\begin{bmatrix}A & {- C} \\{- A} & {- C}\end{bmatrix}}.}$

Using q_(n), a maximum likelihood (ML) based ACFO and CIR estimator canbe formulated. The ACFO is estimated as

${\hat{\varphi}}_{d} = {\arg {\min\limits_{\varphi}{\left( {{q_{n}^{H}\left\lbrack {I_{2N} - {{F(\varphi)}\left( {{F^{H}(\varphi)}{F(\varphi)}} \right)^{- 1}{F^{H}(\varphi)}}} \right\rbrack}q_{n}} \right).}}}$

{circumflex over (φ)}_(d) can be estimated using a grid search.

It is to be noted that, for the pilot symbols used in step 402, thematrix F^(H)(φ)F(φ) is given by

F ^(H)(φ)F(φ)=NI _(2(P+1).)

This implies that the inverse of F^(H)(φ)F(φ) need not be computed forevery search point.

Hence the ACFO {circumflex over (φ)}_(d) can be estimated as

${\hat{\varphi}}_{d} = {\arg {\min\limits_{\varphi}{\left( {{q_{n}^{H}\left\lbrack {I_{2\; N} - {\frac{1}{N}{F(\varphi)}{F^{H}(\varphi)}}} \right\rbrack}q_{n}} \right).}}}$

It can be seen that the ACFO {circumflex over (φ)}_(d) estimation at thedestination is not computationally demanding as no inverse matrixcomputation needs to be done for each search point.

Once the ACFO {circumflex over (φ)}_(d) is estimated, vector h_(F) canbe estimated as

${\hat{h}}_{F} = {\frac{1}{N}{F\left( {\hat{\varphi}}_{d} \right)}{F^{H}\left( {\hat{\varphi}}_{d} \right)}{q_{n}.}}$

Joint ACFO (φ_(r)+φ_(d)) Estimation at the Destination

In step 430, joint ACFO (φ_(r)+φ_(d)) estimation is performed at thedestination for the Cyclic Prefix Scheme 2. The (N×1) received signalvectors at destination (without ACFO compensation at relay) can bewritten as follows:

r _(D,2n) =e ^(j(2n(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(n)(φ_(d)+φ_(r))[α_(n) {hacek over (H)} _(1,D) H _(S,1) W _(N) ^(H) x_(2n)+γ^(n) {hacek over (H)} _(2,D) G _(S,2)(W _(N) ^(H) x _(2n+1))*]

r _(D,2n+1) =e ^(j((2n+1)(N+P) ² ^()+P) ² ^()(φ) ^(d) ^(+φ) ^(r) ⁾ Z_(N)(φ_(d)+φ_(r))[α_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)} _(1,D) H_(S,1) W _(N) ^(H) x _(2n+1)−γ_(n) e ^(jP) ¹ ^(φ) ^(r) {hacek over (H)}_(2,D) G _(S,2)(W _(N) ^(H) x _(2n))*]{tilde over (p)} _(D,2n+1,)

where {hacek over (H)}_(1,D) and {hacek over (H)}_(2,D) respectively are(N×N) circulant matrix with Z_(N)(−φ_(r))[h_(1,D) ^(T),0_(1×(N-L) ₂₎]^(T) and Z_(N)(−φ_(r))[h_(2,D) ^(T), 0_(1×(N-L) ₂ _()]) ^(T) as theirfirst column vectors, and scalars α_(n) and γ_(n) are defined asfollows:

α_(n)=e^(j(2n+1)P) ¹ ^(φ) ^(r)

γ_(n)=e^(j((4n+2)(N+P)−2nP) ¹ ^(−1)φ) ^(r.)

It is defined that φ_(f)=φ_(d)+φ_(r). We have

$\begin{matrix}{q_{n} = \left\lbrack {r_{D,{2n}}^{T},r_{D,{{2n} + 1}}^{T}} \right\rbrack^{T}} \\{{= {{{\overset{\sim}{F}\left( {\varphi_{f},\varphi_{r}} \right)}{\overset{\sim}{h}}_{F}} + e_{n}}},}\end{matrix}$

where the (2N×2(P+1)) matrix {tilde over (F)}(φ^(f), φ_(r)) is given by

${\overset{\sim}{F}\left( {\varphi_{f},\varphi_{r}} \right)} = {{\frac{^{{j{({{2\; {n{({N + P_{2}})}}} + P_{2}})}}\varphi_{f}}}{\sqrt{2}}\begin{bmatrix}{Z_{N}\left( \varphi_{f} \right)} & 0_{N \times N} \\0_{N \times N} & {^{{j{({N + P_{2}})}}\varphi_{f}}{Z_{N}\left( \varphi_{f} \right)}}\end{bmatrix}}{\quad\begin{bmatrix}{\alpha_{n}A} & {{- \gamma_{n}}C} \\{{- \alpha_{n}}^{j\; P_{1}\varphi_{r}}A} & {{- \gamma_{n}}^{j\; P_{1}\varphi_{r}}C}\end{bmatrix}}}$

and {tilde over (h)}_(F) is a (2(P+1)×1) vector constructed as

{tilde over (h)} _(F)=[({hacek over (h)} _(1,D) *h _(S,1))^(T),({hacekover (h)} _(2,D)*ζ(h* _(S,2)))^(T)]^(T)

with {hacek over (h)}_(1,D)=Z_(L) ₂ (−φ_(r))h_(1,D) and {hacek over(h)}_(2,D)=Z_(L) ₂ (−φ_(r))h_(2,D). It can be shown that

{tilde over (F)} ^(H)(φ_(f),φ_(r)) {tilde over (F)}(φ _(f),φ_(r))=NI_(2(P+1).)

The Maximum Likelihood estimate for φ_(f) is obtained as

${\hat{\varphi}}_{f} = {\arg {\min\limits_{\varphi}\left( {{q_{n}^{H}\left\lbrack {I_{2\; N} - {\frac{1}{N}{\overset{\sim}{F}\left( {\varphi,\varphi_{r}} \right)}{{\overset{\sim}{F}}^{H}\left( {\varphi,\varphi_{r}} \right)}}} \right\rbrack}q_{n}} \right)}}$

and {tilde over (h)}_(F) is estimated as

${\hat{\overset{\sim}{h}}}_{F} = {\frac{1}{N}{\overset{\sim}{F}\left( {{\hat{\varphi}}_{f},\varphi_{r}} \right)}{{\overset{\sim}{F}}^{H}\left( {{\hat{\varphi}}_{f},\varphi_{r}} \right)}{q_{n}.}}$

While example embodiments of the invention have been described indetail, many variations are possible within the scope of the inventionas will be clear to a skilled reader. Variations can be made, forexample to parameters such as the number of carriers, the cyclic prefixlengths P, P₁ and P₂, the coding technique used at the relay station, orthe way in which the product channel is estimated. Variations can alsobe made to the design of the pilot symbols used. Further, the CP schemesneed not necessary use space-time coding and other forms of coding maybe used.

1. A method performed by a relay station having multiple antennae, ofrelaying data from a source to a destination, the method comprising thesteps of: using the multiple antennae to receive a message sent by thesource, thereby forming multiple respective received signals, themessage containing the data and comprising a first cyclic prefix havinga length based on channel impulse response of respective channelsbetween the source and the multiple antennae of the relay station;removing the first cyclic prefix from the received signals; encoding thereceived signals to form multiple Alamouti-coded second signals;inserting a second cyclic prefix into the multiple Alamouti-coded secondsignals; and transmitting the multiple Alamouti-coded second signalswith the second cyclic prefix to the destination, the Alamouti-codedsecond signals being used for performing carrier frequency offset (CFO)compensation to the message at the destination.
 2. A method performed bya relay station having multiple antennae, of relaying data from a sourceto a destination, the method comprising the steps of: using the multipleantennae to receive a message sent by the source, thereby formingmultiple respective received signals, the message containing the dataand comprising a first cyclic prefix; removing part of the cyclic prefixfrom the received signals; encoding the received signals to formmultiple second signals; and transmitting the multiple second signalswith the remaining part of the cyclic prefix to the destination.
 3. Amethod of relaying a message according to claim 2, wherein the receivedsignal comprises a first received signal from a first of the antennae ofthe relay station and a second received signal from a second of theantennae of the relay station, the step of encoding the received signalsinvolves combining the first received signal with the second receivedsignal to form the multiple second signals.
 4. A method of relaying amessage according to claim 3, wherein the step of encoding the receivedsignals further comprises the step of obtaining a complex conjugate ofthe first received signal.
 5. A method of relaying a message accordingto claim 3, wherein the step of encoding the received signals furthercomprises the step of reversing the sequence of symbols within the firstreceived signal.
 6. A method of relaying a message according to claim 5,wherein the step of reversing the sequence of symbols within the firstreceived signal further comprises storing the first received signal in ashift register and then reading the shift register in a reversed order.7. A method of relaying a message according to claim 3, wherein the stepof encoding the received signals further comprises the step of negatingthe first received signal.
 8. A method of relaying a message accordingto claim 1, wherein the received signals are encoded with space-timecoding to form the multiple second signals.
 9. A method of relaying amessage according to claim 8, wherein the space-time coding is Alamouticoding.
 10. A method of relaying a message according to claim 1, furthercomprising the step of performing carrier frequency offset (CFO)compensation to the message at the relay station.
 11. A method ofrelaying a message according to claim 1, further comprising the step ofperforming CFO compensation to the message at the destination.
 12. Amethod of relaying a message according to claim 1, wherein the relaystation having multiple antennae is comprised of two relay sub-stationseach having at least one antenna, the two relay sub-stations configuredto perform information passing between each other.
 13. A method ofrelaying data from a source to a destination via a relay station havingmultiple antennae, the method comprising the steps of: (i) the sourcetransmitting the data within a message comprising a first cyclic prefixhaving a length based on channel impulse response of respective channelsbetween the source and the multiple antennae of the relay station; (ii)the relay station: receiving the message using the multiple antennae,thereby forming multiple respective received signals; removing the firstcyclic prefix from the received signals; encoding the received signalsto form multiple Alamouti-coded second signals; inserting a secondcyclic prefix into the multiple Alamouti-coded second signals;transmitting the Alamouti-coded second signals with the second cyclicprefix to the destination; and (iii) the destination receiving thesecond signals and extracting the data, wherein the Alamouti-codedsecond signals is used for performing carrier frequency offset (CFO)compensation to the message at the destination.
 14. A method of relayingdata from a source to a destination via a relay station having multipleantennae, the method comprising the steps of: (i) the sourcetransmitting the data within a message comprising a first cyclic prefix;(ii) the relay station: receiving the message using the multipleantennae, thereby forming multiple respective received signals; removingpart of the cyclic prefix from the received signals; encoding thereceived signals to form multiple second signals; transmitting themultiple second signals with the remaining part of the cyclic prefix tothe destination; and (iii) the destination receiving the second signalsand extracting the data.
 15. A method of relaying data according toclaim 14, further comprising the step of performing CFO compensation tothe message at the destination, thereby compensating both for CFOpresent from the source to the relay station and for CFO present fromthe relay station to the destination.
 16. A method of estimating channelstate information for a wireless communication channel comprising asource, a relay station having multiple antennae and a destination, themethod comprising the steps of: a first of the antennae of the relaystation receiving a first training signal from the source; a second ofthe antennae of the relay station receiving a second training signalfrom the source; the relay station: (i) encoding the first trainingsignal and the second training signal with space-time encoding to formmultiple Alamouti-coded relay training signals; and (ii) transmittingthe multiple Alamouti-coded relay training signals in at least onesymbol interval; and the destination receiving the relay trainingsignals and from the Alamouti-coded relay training signals estimatingthe channel state information, wherein the Alamouti-coded relay trainingsignals are also used for performing carrier frequency offset (CFO)compensation at the destination.
 17. A method of estimating channelstate information for a wireless communication channel according toclaim 16, further comprising the step of estimating a first carrierfrequency offset (CFO) parameter at the relay station by combining thefirst training signal and the second training signal.
 18. A method ofestimating channel state information for a wireless communicationchannel according to claim 17, wherein the combining the first trainingsignal and the second training signal performs a conjugate transpose tothe first training signal.
 19. A method of estimating channel stateinformation for a wireless communication channel according to claim 16,wherein the first training signal comprises a first pilot signal, andthe second training signal comprises a second pilot signal, the secondpilot signal a negative of the first pilot signal.
 20. A method ofestimating channel state information for a wireless communicationchannel according to claim 17, further comprising the step of receivingat a destination station a combined training signal, the combinedtraining signal comprising the multiple relay training signals and acombined noise signal.
 21. A method of estimating channel stateinformation for a wireless communication channel according to claim 20,wherein the combined noise signal comprises a second carrier frequencyoffset (CFO) estimated by the destination.
 22. A method of estimationchannel state information for a wireless communication channel accordingto claim 21, wherein the second CFO is estimated by a maximum likelihoodestimation.
 23. A method of estimating channel state information for awireless communication channel according to claim 22, wherein themaximum likelihood estimation is a grid search.
 24. A method ofestimation channel state information for a wireless communicationchannel according to claim 17, wherein the relay station is configuredto perform a CFO compensation using the first CFO parameter.
 25. Amethod of estimation channel state information for a wirelesscommunication channel according to claim 21, wherein the destinationstation is configured to perform a CFO compensation using the second CFOparameter.
 26. A method of estimation channel state information for awireless communication channel according to claim 21, wherein the firstCFO parameter estimated at the relay station is forwarded to thedestination, the destination configured to perform a joint CFOcompensation using the first CFO parameter and the second CFO parameter.27. A method of transmitting data along a wireless communication channelfrom a source to a destination via a relay station having multipleantenna, the method comprising: estimating channel information of thechannel by a method according to claim
 16. transmitting along thewireless communication channel a message containing the data; andextracting the data from the message using the estimated channelinformation.
 28. A relay station for relaying data from a source to adestination, and having multiple antennas, the relay station beingarranged to perform a method according to claim
 1. 29. A systemcomprising a source, a destination, and a relay station for relayingdata from the source to the destination and having multiple antennas,the system being arranged to perform a method according to claim
 13. 30.An integrated circuit (IC) for a relay station configured for relayingdata from a source to a destination, said relay station having multipleantennae configured to receive a message sent by the source and therebyforming multiple respective received signals, the message containing thedata and comprising a first cyclic prefix having a length based onchannel impulse response of respective channels between the source andthe multiple antennae of the relay station, the IC comprising: aninterface configured to receive the multiple respective received signalsfrom the multiple antennae; a first processing unit configured to removethe first cyclic prefix from the received signals; an encoder configuredto encode the received signals to form multiple Alamouti-coded secondsignals; a second processing unit configured to insert a second cyclicprefix into the multiple Alamouti-coded second signals; and theinterface further configured to send the multiple Alamouti-coded secondsignals with the second cyclic prefix to the multiple antennae fortransmission to the destination, wherein the Alamouti-coded secondsignals is used for performing carrier frequency offset (CFO)compensation to the message at the destination.
 31. An integratedcircuit (IC) for a relay station configured for relaying data from asource to a destination, said relay station having multiple antennaeconfigured to receive a message sent by the source and thereby formingmultiple respective received signals, the message containing the dataand comprising a first cyclic prefix, the IC comprising: an interfaceconfigured to receive the multiple respective received signals from themultiple antennae; a processing unit configured to remove part of thecyclic prefix from the received signals; an encoder configured to encodethe received signals to form multiple second signals; the interfacefurther configured to send the multiple second signals with theremaining part of the cyclic prefix to the multiple antennae fortransmission to the destination.